I agree the OUTPUT clause is the way to go.
Something along these lines should work
Declare @Results Table
(
RequestQueueID bigint not null,
ScopeRequestID bigint not null
)
Insert Into dbo.RequestQueue
Select
From [dbo].[udtt_Request]
Output Inserted.RequestQueueID, ScopeRequestID Into @Results
Insert Into dbo.RequestProperties
Select , R.RequestQueueID
From [dbo].[udtt_RequestProperties] As RP
Inner Join @Results As R ON Rp.ScopeRequesID = R.ScopeRequesID